Positive invariant and global exponential attractive sets of neural networks with time-varying delays

In this paper, global exponential stability in Lagrange sense is further studied for various continuous-time delayed recurrent neural network with two different types of activation functions. Based on the parameters of the systems, detailed estimation of global exponential attractive sets and positive invariant sets are presented without any hypothesis on the existence. It is also verified that outside the global exponential attracting set; i.e., within the global attraction domain, there is no equilibrium state, periodic state, almost periodic state, and chaos attractor of the neural network. These theoretical analysis narrows the search field of optimization computation, associative memories, chaos control and synchronization and provide convenience for applications.